Improvement of some features of finite elements with embedded discontinuities

This paper shows an analysis of the principal features of finite elements with embedded discontinuities. Particularly, two families of this kind of elements are analyzed, kinematically optimal symmetric and statically and kinematically optimal non-symmetric. The analyzed features are the variational formulation, damage model and how the discontinuity is introduced. A new definition of traction vector for symmetric family, dependent on the discontinuity length and the angle, is given. It is shown that kinematics and equilibrium are satisfied, without the problem of fictitious tractions as stated in the literature. To show the validity of this symmetric formulation, representative numerical examples illustrating the performance of the proposed formulation are presented.